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- W1816170485 abstract "We study class of Levy processes having distributions being indentifiable by moments. We define system of polynomial martingales newline $left{ M_{n}(X_{t},t),mathcal{F}_{leq t}right} _{ngeq 1},$ where $% mathcal{F}_{leq t}$ is a suitable filtration defined below. We present several properties of these martingales. Among others we show that $% M_{1}(X_{t},t)/t$ is a reversed martingale as well as a harness. Main results of the paper concern the question if martingale say $M_{i}$ multiplied by suitable determinstic function $mu _{i}(t)$ is a reversed martingale. We show that for $ngeq 3$ $M_{n}(X_{t},t)$ is a reversed martingale (or orthogonal polynomial) only when the Levy process in question is Gaussian (i.e. is a Wiener process). We study also a more general question if there are chances for a linear combination (with coefficients depending on $t)$ of martingales $M_{i},$ $iallowbreak =allowbreak 1,ldots ,n$ to be reversed martingales. We analyze case $% nallowbreak =allowbreak 2$ in detail listing all possible cases." @default.
- W1816170485 created "2016-06-24" @default.
- W1816170485 creator A5012467725 @default.
- W1816170485 date "2012-12-13" @default.
- W1816170485 modified "2023-09-27" @default.
- W1816170485 title "L'evy processes, martingales, reversed martingales and orthogonal polynomials" @default.
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